Make logo clearer

Closed - This job posting has been filled and work has been completed.

Job Description

I have a logo which is on our site rubbledesigns.com.au/newsite
but the bottom half of the logo which overlaps the header looks pixelated.

I want this to ideally not be pixelated at all, but not sure if this is possible.

The image is 120 x 120 px. I have it in a .psd as well as .ai file